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Automatically send Claude Code conversations and tool calls to Braintrust. View nested activity records that connect each session, conversation exchange, and operation, including file reads, edits, and terminal commands, to inspect how coding work unfolded.

한국어 요약은 준비 중입니다. 영어 요약을 표시하고 있습니다.

• Review the flow of a Claude Code session
• Inspect tool calls alongside conversation exchanges
• Set up automatic session logging in Braintrust

Work through topology problems about connectedness, the property of a space having no separation into two nonempty open parts. It outlines proof strategies, path construction, and connected components, with command examples for symbolic calculation and proof tools.

한국어 요약은 준비 중입니다. 영어 요약을 표시하고 있습니다.

• Choosing a strategy for a connectedness proof
• Constructing paths between points in a convex set
• Proving a union of connected sets is connected

Plan solutions to topology problems involving open sets and continuous maps. Choose criteria based on distances or preimages, the points mapping into a set, and organize reasoning about interiors, closures, boundaries, and epsilon-delta conditions.

한국어 요약은 준비 중입니다. 영어 요약을 표시하고 있습니다.

• Proving that a set is open
• Checking continuity using preimages
• Organizing interiors, closures, and boundaries

Work through limits in real analysis by choosing among substitution, algebraic manipulation, derivative-based methods, and bounding arguments. The skill also guides rigorous epsilon-delta proofs and provides commands for symbolic calculations and proof checks.

한국어 요약은 준비 중입니다. 영어 요약을 표시하고 있습니다.

• Choose a method for solving a limit
• Simplify an indeterminate expression
• Check bounds for the squeeze theorem

Organize topology problems about compactness, a property defined through finite selections from open covers. Choose tests suited to the space, examine products, and apply compactness to continuous images and maximum or minimum values.

한국어 요약은 준비 중입니다. 영어 요약을 표시하고 있습니다.

• Check compactness of a subset of Euclidean space
• Examine compactness through sequences or open covers
• Study compactness of product spaces

Work through matrix eigenvalue problems, from the characteristic polynomial, whose roots give the eigenvalues, to finding eigenvectors. Follow a structured process to check the results and examine algebraic and geometric multiplicities.

한국어 요약은 준비 중입니다. 영어 요약을 표시하고 있습니다.

• Finding a matrix's eigenvalues and eigenvectors
• Computing a characteristic polynomial
• Checking eigenvalue and eigenvector results

Plan solutions to modular arithmetic problems, which involve integer remainders. Choose methods for modular inverses, simultaneous congruences, powers, quadratic residues, and primitive roots, with example commands for symbolic calculations and checking mathematical claims.

한국어 요약은 준비 중입니다. 영어 요약을 표시하고 있습니다.

• Finding a modular inverse with the extended Euclidean algorithm
• Solving simultaneous congruences with the Chinese Remainder Theorem
• Simplifying powers using Euler's Theorem

Work through matrix problems in linear algebra by identifying matrix types and choosing suitable calculations. The skill covers multiplication, inverses, determinants, linear systems, and decompositions that express a matrix as simpler components.

한국어 요약은 준비 중입니다. 영어 요약을 표시하고 있습니다.

• Identifying matrix types and properties
• Calculating matrix products, inverses, and determinants
• Solving systems of linear equations

Work through natural transformation problems in category theory by checking component maps and compatibility conditions. The skill outlines strategies for natural isomorphisms, composition, and the Yoneda lemma, with references for expressing and checking work in Lean 4.

한국어 요약은 준비 중입니다. 영어 요약을 표시하고 있습니다.

• Check the naturality of a transformation
• Examine whether a transformation is a natural isomorphism
• Study composition in functor categories

Review progress while solving a math problem by organizing previous attempts, checking intermediate results, and assessing growing complexity. The skill recommends whether to continue, adjust the approach, switch strategies, or tackle a smaller problem first.

한국어 요약은 준비 중입니다. 영어 요약을 표시하고 있습니다.

• Review an approach when stuck on a math problem
• Assess calculations that keep getting more complicated
• Check intermediate results

Work through operator theory problems in functional analysis with structured steps for boundedness, adjoints, spectra, and compactness. Includes example commands for symbolic calculations and proof checks using SymPy and Z3.

한국어 요약은 준비 중입니다. 영어 요약을 표시하고 있습니다.

• Check whether an operator is bounded
• Work out an adjoint operator
• Study the spectrum of a self-adjoint operator

Helps select graph algorithms for shortest paths, minimum spanning trees, network flow, and coloring. Provides decision guides and example commands for symbolic calculations and checking mathematical properties.

한국어 요약은 준비 중입니다. 영어 요약을 표시하고 있습니다.

• Choosing a shortest path algorithm
• Planning a minimum spanning tree solution
• Setting up network flow equations

Choose approaches for prime number problems, including primality testing, factorization, and prime distribution. The skill outlines relevant algorithms and theorems, with commands for symbolic calculation and checking mathematical claims.

한국어 요약은 준비 중입니다. 영어 요약을 표시하고 있습니다.

• Choosing a primality testing method
• Selecting a factorization approach
• Studying prime distribution and gaps

Study source coding, the information theory behind data compression. The skill guides problems involving Huffman codes, average code length, prefix-code constraints, arithmetic coding, and the tradeoff between compression rate and distortion, with calculation and proof command examples.

한국어 요약은 준비 중입니다. 영어 요약을 표시하고 있습니다.

• Construct Huffman codes from symbol probabilities
• Compare average code length with entropy
• Check code lengths using Kraft's inequality

Solve complex analysis problems by choosing residue calculations for different singularities, points where a function is not analytic. The skill covers limits, derivatives, Laurent series, and contour integrals using the residue theorem, with Sympy and Z3 command examples.

한국어 요약은 준비 중입니다. 영어 요약을 표시하고 있습니다.

• Calculating residues at simple and higher-order poles
• Determining the order of a pole
• Finding residues at essential singularities using Laurent series

Review the technology choices in an implementation plan using past project outcomes and web research. Produce a report that identifies outdated approaches, deprecated tools, and security concerns, with supporting sources and suggested alternatives.

한국어 요약은 준비 중입니다. 영어 요약을 표시하고 있습니다.

• Reviewing library choices before implementation
• Checking for deprecated technologies and security concerns
• Comparing a proposed design with past project outcomes

Give new users a practical introduction to what the agent can help with, including coding, memory, research, and planning. Explain natural ways to ask for work, recall earlier lessons, and prepare handoffs for later sessions.

한국어 요약은 준비 중입니다. 영어 요약을 표시하고 있습니다.

• Explore what the agent can help with
• Learn how to make a first request
• Learn how to recall lessons from earlier work

Check whether infrastructure code actually runs when a user triggers it. Trace calls from hooks or commands through scripts and modules, verify registration and permissions, and test the complete path to uncover unreachable code.

한국어 요약은 준비 중입니다. 영어 요약을 표시하고 있습니다.

• Checking whether a newly added hook actually runs
• Tracing calls from a command to module execution
• Finding unused modules and missing registrations

Build understanding of mathematical ideas before calculating. The skill guides you through concrete examples, diagrams, simpler cases, and analogies, then summarizes the intuition and suggests a next step with a check.

한국어 요약은 준비 중입니다. 영어 요약을 표시하고 있습니다.

• Understanding the meaning behind a formula
• Exploring geometric interpretations
• Starting an abstract problem with small examples

Choose a mathematical approach for a problem you do not yet know how to model. Guided questions clarify change, uncertainty, optimization goals, and required precision, leading to a recommended framework, starting equations, tools, and related skills.

한국어 요약은 준비 중입니다. 영어 요약을 표시하고 있습니다.

• Choosing a mathematical approach for a real-world problem
• Deciding how to model discrete or continuous change
• Selecting methods for uncertainty or optimization

Work through graduate-level problems using Rudin's Real and Complex Analysis. The skill guides theorem selection for measure theory, integration, and complex analysis, with commands for textbook searches, symbolic calculations, and verification.

한국어 요약은 준비 중입니다. 영어 요약을 표시하고 있습니다.

• Choosing theorems for limits and integrals
• Working through contour integrals and residues
• Studying function spaces and linear operators

Guides work on categories and functors by checking definitions, composition rules, and structure-preserving properties. Explains common functor types and provides examples for verifying proofs with Lean 4 and Mathlib.

한국어 요약은 준비 중입니다. 영어 요약을 표시하고 있습니다.

• Checking whether a construction satisfies category axioms
• Verifying that a mapping is a functor
• Distinguishing common types of functors

Choose approaches to Hilbert space problems in functional analysis using orthogonal decomposition, projection, and representation theorems. The skill provides a decision tree and command examples for inner product calculations and proof tasks.

한국어 요약은 준비 중입니다. 영어 요약을 표시하고 있습니다.

• Choosing an approach to Hilbert space exercises
• Studying orthogonal decomposition and projection
• Working through the Riesz representation theorem

Match code investigation questions to the appropriate tldr command. Find ways to inspect files, function calls, branching, variable flow, and line dependencies, helping you explore a project or investigate a bug.

한국어 요약은 준비 중입니다. 영어 요약을 표시하고 있습니다.

• Exploring files, functions, and classes
• Tracing function calls
• Investigating variable flow during debugging